With all of these restrictions, it seems like you're only possibility is to have the answers as audio too. Perhaps you hover over one button and you hear "Yes, the sky is blue," and you hover over the other and you hear "No, the sky is not blue."
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Joseph MansfieldSep 21 '13 at 23:28

Would it be possible to approach the problem in a different way? Instead of asking questions where the user decides just yes or no, make them state their choice by affirming text.

For example, instead of:

Does a pilot's license require the applicant to know the complete rulebook?
[Yes]
[No]

use:

A pilot's license requires the applicant to know
[the complete rulebook]
[the important parts of the rulebook]

Using yes or no symbols can be confusing, especially if the question includes negation (aka. "Do you really want to quit and not safe your work progress? Yes/No"). Reiterating the user's intent in a short phrase can be more understandable (i.e. "Save before quitting/Dismiss changes")

This sort of evades your question, but I think there is a good reason why there is no universally agreed upon sign for yes and no. These short binary answers always have meaning only in their context and not by themselves, thus creating a symbol for them is hard.

Considering your edited question my answer and examples are less applicable to your problem. Maybe one similar approach to solve the problem transferred to your situation would be to offer the users choices that still are more explicit than just a "yes/no" or attempted icon for those answers. For example your question "Is the sky blue?" could have two images as choices, one bright blue daylight scene and one orange-red sunset. This way you make the user repeat and affirm their choice.

Agree, Yes and No also requires users to read question (do more work). More expressive controls could make it easier since you may not need to read the questions. Unless it's one of a very generic forms where you know I just need to says "No/Yes" for all of the questions.
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Anna RoubenSep 18 '13 at 20:17

Even in the first example, it could be made into a statement, "A pilot is required to know the complete rulebook," followed by the tick and cross for "correct" and "incorrect". But presenting real multiple-choice questions is by far the best solution: infinitely scalable and probably easily localised.
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Andrew LeachSep 19 '13 at 7:52

3

See my update. Questions are audio, so we want to keep the answers as simple as possible (also the audio is all finished and must be answered Y/N)
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Clay NicholsSep 19 '13 at 11:44

Shaking to indicate "no" is widespread, and appears in a large number of diverse cultural and linguistic groups. Areas in which head shaking generally takes this meaning include Indian subcontinent, Middle East, Africa, Southeast Asia, Western Europe, and North America.

Nodding to indicate "yes" is widespread, and appears in a large number of diverse cultural and linguistic groups. Areas in which nodding generally takes this meaning include the Indian subcontinent (note that the head bobble also shows agreement there), Iran, Southeast Asia, Western Europe, Latin America and North America.

For cultures with different meanings for head shake/nod, you’ll have to adjust it accordingly. Of course this is only possible if you know the background of your visitors. If you expect visitors from many different cultures, you could start with an opening question like "Which gesture represents yes for you?" and let your visitors choose.

But to 'calibrate' the animations to the culture, one would have to be able to read, which isn't a given in this situation.
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DA01Sep 19 '13 at 18:03

@DA01: No, the opening question can be read out, of course (as it’s the case for all the other questions, too).
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unorSep 20 '13 at 8:57

Some educational software I used growing up (don't recall which) took this approach. A dialog box showed up (with the prompt being read aloud), but instead of yes/no buttons, there was an animated face nodding up and down (yes) and an animated face nodding side to side (no). There was also the words "Yes" and "No below each face respectively so that kids might learn to recognize the words. Worked well enough for me as a kid, although if your target audience includes cultures with different head gestures, you'll have to have an opening question to determine the locale.
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ThunderforgeSep 24 '13 at 19:31

The dire restriction here is implicit, that a single pair of symbols must work for all cultures.
If you had several symbol pairs, and as part of the translation you could provide links to the locally appropriate pair of symbols then you might use the preferred choice for each culture.
OK, the i18n software does not allow for images translation (or does it?).
If not then have two hidden items like "yes_icon_URL" and "no_icon_URL" translated to the appropriate values, and use a small bit of js to set the button backgrounds in a localized fashion with the URLs contained there.

I'm in the UK, their 'No' looks to me like 'prohibited', not 'no'. Mind, I'm not in education and, as a driver, I see that sign on the roadside a lot, where it means just that.

You've given some context with referencing educational software but not said what age group. I work in that realm and with primary school age kids. I'd definitely not go with green squares, although the colour is right, obviously - for those without colourblindness, at least - the shape means nothing.

I'd go with ticks and crosses first and then vote for the smiliy face.